> On Tuesday, 15 October 2013 10:19:50 UTC+2, Wisely Non-Theist wrote:> > All Cantor says is that if an infinite list of reals is created it will not > > contain all reals. > > That is the same that I say, because there is nothing like "all reals". But > he thinks that he can construct another one that does not fit into the list > since it is closed.

Note that if an infinite list of naturals is created, there need not be any naturals not listed in it.

Note that if an infinite list of rationals is created, there need not be any ratinals not listed in it.

All Cantor says is that if any infinite list of reals is created it will necessarily omit at least one real.

And Cantor has proved it far beyond WM's poorer power to disprove things.> > > So that if you claim that no such infinite list can ever exist, then > > Cantor's proof is valid. > > No. By pure accident it has the same result only.

That "pure accident" is a proof far beyond WM's power to disprove,at least outside his wild weird world of WMytheology >

> > Then at least two are required, i.e., contain more than either of them.

Show me two lines that contain more that the larger.

On the other hand, the set of all odd numbered lines ( having an odd largest value) unions to give al members of all lines.> > > Any set of infinitely many lines.> > Has a first line. And includes all members of all lines.

> Any set of lines which are required, i.e., which contain > more natural than either of them, has a first line.

Only because the set of all infinitely many lines is well -ordered by inclusion, so any non-emyptu set of it has a first member, but that does not justify WM's insanity on the subject.

> If there are no such > required lines, then either *all naturals* are in one line or do not exist.

WM may only claim that that holds in his wild weird world of WMytheology, as everywhere else it is trivially false.> > For example. the set of all odd numbered lines and the disjont set of all > even numberd ines will each sperately contain all the numbers in all of the > lines.> > Plwease stop your unproven claims

I will stop my provable, even if occasionally unproven, claims only when WM has stopped his unproven and provably unprovable claims about what goes on OUTSIDE of his his wild weird world of WMytheology.

> but prove that inclusion monotony and logic > are false.

What WM claims for inclusion monotony is nonsense outside of his wild weird world of WMytheology, and logic does not exist there, but only outside of it.> > > So, since those two set of lines are clarly disjoint sets , there is NO > > single line which is required.> > Then at least tow lines of one or of both sets are required.

Two lines are not enough. Three lines are not enough.A finite set of lines is not enough.Nothing less numerous that an infinite set of lines is a large enough set of lines.> > > WM cannot produce any finite set of lines which will contain all members of > > all lines,> > Correct.> > > nor can WM produce any infinite set of lines which does not contain all > > members of all lines.> > Incorrect.

Then produce such a set, WM,and prove me wrong, or admit that WM cannot produce any infinite set of lines of WM's very own matrix that does NOT contain all members of all lines of WM's very own matrix.

And until WM can produce an infinite set of lines which does NOT contain all members of all lines, he remains WRONG!> > > > The alternative to no one line containig all , is not that two lines have > > to contain more than either of of them but that more lines than are in any > > finite set of lines are necessary to contain all of members of all lines.> > If there are many lines required to contain more than either of them, then > there must be a first line of this set.

Any subset of a well-ordered set is also well orered. So what?> > Handwaving belief in infinity with violating mathematical priciples

Belief in infinities does not violate any of the principles that govern proper mathematics, it only violates those idiotic anti-principles that seem to misgovern WM's wild weird world of WMytheology.

> and > claiming infinitely many lines where not even two can be shown is not > convincing.